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The best option short of opening up the wall is to screw a piece of 3/4" plywood (big enough to accommodate the bracket and to bridge the studs)to the studs then screw the mounting bracket to the plywood. You can paint the plywood the same color as the wall to make it less conspicuous if you like. If you want the bracket flush with the drywall then you have to cut the wall open and screw a 2 x 3 cleat to each stud holding it back 3/4" from the face of the drywall then screw your 3/4" plywood to the cleats.